Computes the Sharpe Ratio Information Coefficient of Paulsen and Soehl, an asymptotically unbiased estimate of the out-of-sample Sharpe of the in-sample Markowitz portfolio.
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Let X be an observed T x k matrix whose rows are i.i.d. normal. Let mu and Sigma be the sample mean and sample covariance. The Markowitz portfolio is
w = Sigma^-1 mu,
which has an in-sample Sharpe of zeta = sqrt(mu' Sigma^-1 mu).
The Sharpe Ratio Information Criterion is defined as
SRIC = zeta - ((k-1) / (T zeta)).
The expected value (over draws of X and of future returns) of the SRIC is equal to the expected value of the out-of-sample Sharpe of the (in-sample) portfolio w (again, over the same draws.)
The Sharpe Ratio Information Coefficient.
Steven E. Pav email@example.com
Paulsen, D., and Soehl, J. "Noise Fit, Estimation Error, and Sharpe Information Criterion." arxiv preprint (2016): http://arxiv.org/abs/1602.06186
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